find the sum of all the natural numbers between 200 and 300 which are divisible by 4.

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The number between 200 and 300 which are divisible by 4 are 204, 208,.........,296.

204, 208,.........,296 are in AP.

Here a = 204 and d = 4

Let 296 be the n^th term of the AP.

a_n = 296

∴ 204 +(n – 1) × 4 = 296                               ( a_n = a + (n – 1)d)

⇒ 4(n – 1) = 296 – 204 = 92

⇒ n – 1 = 23

⇒ n = 24

Sum of all natural number between 200 and 800 which are divisible by 4

= 12 (408 + 23 × 4)

= 12 (408 + 92)

= 12 × 500

= 6000